Simplify the following expression: $q = \dfrac{-4z - 6}{4z + 2} - \dfrac{-6z - 18}{4z + 2}$
Since the expressions have the same denominator we simply subtract the numerators: $q = \dfrac{-4z - 6 - (-6z - 18)}{4z + 2}$ Distribute the negative sign: $q = \dfrac{-4z - 6 + 6z + 18}{4z + 2}$ Combine like terms: $q = \dfrac{2z + 12}{4z + 2}$ Simplify by dividing numerator and denominator by 2: $q = \dfrac{z + 6}{2z + 1}$